Math Econ Que

Exercise 4

The farmer above can purchase two types of fertilizer.

A 50lb bag of crescent fertilizer has 5 units of nitrogen, 15 units of phosphorous, and 5 units of potash and cost $12.

A 50lb bag of Island fertilizer has 10 units of nitrogen, 10 units of phosphorous and 30 units of potash and costs $16.

For a given crop the farmer must make sure that it does not receive more than 100 units of nitrogen and does not receive less than 120 units each of phosphorous and potash.

How many bags of each type of fertilizer should the farmer purchase to minimize his cost ?

Answer:

Name	weight	Nitrogen (red)	Phosphorous (black)	Potash (blue)	cost
Crescent (x)	50	5	15	5	$12
Island (y)	50	10	10	30	$16

The set of equation becomes:

From the graphical representation above: it can be clearly stated that to have all the solutions

So, using the interpreted data:

Name	Nos. of bags	Cost
Crescent (x)	18
Island (y)	9